Question

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $\frac{I_{A}}{I_{B}}$ is equal to

• A. $1:4$
• B. $1:16$
• C. $1:2$
• D. $1:1$

Answer 1

Answer: (D)

The intensity can be given by
$I=2\pi ^{2}\rho ^{2}A^{2}v$
Hence,
$\frac{I_{A}}{I_{B}}=\frac{f_{A}^{2} A_{A}^{2}}{f_{B}^{2} A_{B}^{2}}$
$\frac{I_{A}}{I_{B}}=\left(\frac{1}{2}\right)^{2}\left(\frac{2}{1}\right)^{2}$
$\frac{I_{A}}{I_{B}}=1$